The Compleat Strategyst Being a Primer on the Theory of Games of Strategy

by Williams, J. D.

• ISBN13: 9780486251011
• ISBN10: 0486251012
• Format: Paperback
• Copyright: 1986-05-01
• Publisher: Dover Publications

Summary

This entertaining text is essential for anyone interested in game theory. Only a basic understanding of arithmetic is needed to grasp the necessary aspects of strategy games for two, three, four, and more players that feature two or more sets of inimical interests and a limitless array of zero-sum payoffs.

Table of Contents

PREFACE TO THE REVISED EDITION
PREFACE TO THE FIRST EDITION
CHAPTER 1. INTRODUCTION
  Nature of the Subject
  An Historical Theory
  Lessons and Parallels
  Sectarian Remarks on Method
  Players and Persons
  The Payoff
  Strategies
  The Game Matrix
  Implicit Assumptions
  The Criterion
  Example 1. The Campers
CHAPTER 2. TWO - STRATEGY GAMES
  PART 1: 2 X 2 Games
    The Approach
    Fluctuations
    Saddle-points
    Mixed Strategies
    The Oddment
    Rules for Finding Odds
    Value of the Game
    Scale Effects
    Good Play vs. Poor
    Example 2. The Hidden Object
    Example 3. The Daiquiris
    Example 4. The River Table
    Example 5. The Attack-Defense Game
    Example 6. The Music Hall Problem
    Example 7. The Darkroom
    Example 8. The Birthday
    Example 9. The Huckster
    Example 10. The Squad Car
    Summary of 2 X 2 Methods
    Exercises 1
  PART 2: 2 X m Games
    Saddle-points
    Dominance
    Mixed Strategies
    Graphical Solutions
    Example 11. The Spellers
    Example 12. The Sports Kit
    Example 13. The Hi-Fi
    Chance Devices
    Summary of 2 X m Methods
    Exercises 2
CHAPTER 3. THREE - STRATEGY GAMES
  PART 1: 3 X 3 Games
    Morale-building Discourse
    Saddle-points
    Dominance
    Value of the Game
    Three Active Strategies
    Games We Wish You'd Never Met
    Example 14. Scissors-Paper-Stone
    Example 15. The Coal Problem
    Example 16. The Heir
    Example 17. The Cattle Breeders' Separation
    Example 18. The Date
    Summary of 3 X 3 Methods
    Exercises 3
  PART 2: 3 X m Games
    Method of Solving
    Example 19. The Bass and the Professor
    Example 20. The Bedside Manner
    Example 21. The Chessers
    Summary of 3 X m Methods
    Exercises 4
CHAPTER 4. FOUR - STRATEGY GAMES AND LARGER ONES
  Solution via Revelation
  Saddle-points
  Dominance
  All-strategies-active
  Example 22. The Secondhand Car
  Example 23. The Silviculturists
  Example 24. Color Poker
  Example 25. For Older Children
  Example 26. The Process Server
  Example 27. The Palm Game
  Example 28. The Administrator's Dilemma
  Example 29. The Colonel Blotto Problem
  Example 30. Morra
  Example 31. The Maze
  Example 32. Merlin
  Summary of 4 X m Methods
  Exercises 5
CHAPTER 5. MISCELLANY
  Approximations
  More on Dominance
  Simple Solutions
  Multiple Solutions
  Exercise 6
  On Measurement
  Qualitative Payoffs
  Example 33. Portia
  Example 34. The Lady or the Tiger
  Games Played Only Once
  Symmetric Games
  Linear Programming
  Example 35. The Diet
  Non-zero-sum Games
  Conclusion
CHAPTER 6. GENERAL METHOD OF SOLVING GAMES
  First Example
  Basic Solutions
  Second Example
  Summary of Pivot Method
  How to Check the Work
  Control Sums
APPENDIX
  Table of Random Digits
  Solutions to Exercises
INDEX